Problem: Solve for $x$ and $y$ using substitution. ${5x+5y = 5}$ ${y = 5x-11}$
Solution: Since $y$ has already been solved for, substitute $5x-11$ for $y$ in the first equation. ${5x + 5}{(5x-11)}{= 5}$ Simplify and solve for $x$ $5x+25x - 55 = 5$ $30x-55 = 5$ $30x-55{+55} = 5{+55}$ $30x = 60$ $\dfrac{30x}{{30}} = \dfrac{60}{{30}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {y = 5x-11}\thinspace$ to find $y$ ${y = 5}{(2)}{ - 11}$ $y = 10 - 11$ $y = -1$ You can also plug ${x = 2}$ into $\thinspace {5x+5y = 5}\thinspace$ and get the same answer for $y$ : ${5}{(2)}{ + 5y = 5}$ ${y = -1}$